Solution1 - Answers to HW 1 1. Sample space is composed of...

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Answers to HW 1 1. Sample space is composed of 52 elements such as {A,2,3,4,5,6,7,8,9,10,J,Q,K} associated with 4 different suits. For instance, the probability of event {A,J} is assigned as p(A,J) = 8/52=2/13 2. 1/3; 2/3; b-a, if ba . 3. p(L|U)=0, P(C|U)= 1 7 12 12 31 12 7 = + 4. P(U|C)= 1 1 12 11 3 12 6 = + , P(M|C)= 1 2 6 3 12 6 = + 5. The expected payoff of player 2 is 1 2 2 1 2 0 ( 2) ( 2 2) 1 33 5 5 5 3 55 5 + ++ + = . 6. Each 1,2,4,5 remaining in the urn is equally likely to be drawn with a 1/4 chance. 7. Proportion Duck = 1 3 34 35 2 0 .65 ⋅+⋅= = P(Round|Lamb)= 22 35 16 21 22 11 35 34 .76 == ⋅+⋅ P(Bone|Duck)= 3 1 34 5 13 .38 8. (i) just one positive test result. ( ) ( | ) ( ) 0.95 0.05 (| ) 0.250 ( ) ( | ) ( ) ( |~ ) (~ ) 0.95 0.05 0.15 0.95 p cont p cont p cont p cont p p
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